单自由度含间隙分段线性系统周期运动的倍化分岔

Period-Doubling Bifurcation of Single-Degree-of-Freedom Piecewise-Linearity System with Clearance

研究单自由度含间隙分段线性系统周期运动的倍化分岔现象和混沌行为.求出系统的切换矩阵后,应用Floquet理论分析该系统周期运动发生倍化分岔的条件.通过建立Poincaré映射,用数值方法揭示系统周期运动经倍化分岔通向混沌的现象.结果表明,当激振频率接近临界分岔点时,系统有1个Floquet特征乘子接近-1,系统发生倍周期分岔.

The period-doubling bifurcation and chaos of periodic motions of a single-degree-of-freedom piecewise linear system with clearance was studied. The switching matrix for the system was obtained, and the period-doubling bifurcation of periodic motions was analyzed by the Floquet theory. The poincare map was established, and the period-doubling bifurcations and chaotic behaviors in the nonsmooth system were further investigated by means of numerical simulation. The results show that there is a Floquet multiplier close to - 1 for the system, and period-doubling bifurcations occur when the excitation frequency approaches a critical bifurcation point.